A number of studies have been done regarding propagation of electromagnetic (EM) waves in periodic dielectric structures. It has been suggested that photons in such media can be described by a photonic band theory analogous to electronic band theory in crystals because of the wave nature of photons. One result of a photonic band theory is the possibility of the existence of photonic band gaps in periodic dielectric structures. The presence of a photonic band gap around a particular frequency would mean that propagation of EM waves would be forbidden for all wave vectors (i.e., in every direction) at frequencies within the gap. Spontaneous emission at those frequencies would be inhibited since the photons that would otherwise result cannot propagate. If the frequency of the radiative recombinations of electron-hole pairs in a semiconductor device fell within that photonic band gap, those recombinations would be forbidden. As a result, more carriers would be available in a diode laser for stimulated emission at the lasing frequency, and the efficiency of the laser would be improved. A similar improvement in operating efficiency would also be found in other quantum electronic devices that are limited in efficiency by radiative recombination.
At least one experimenter has reported the existence of a photonic band gap in a structure where dielectric material was arranged in a face-centered-cubic (fcc) lattice structure. That structure had spherical cavities at the lattice sites with another dielectric filling the gaps between the spheres. The filling ratio of the spheres was 86%, that is, slightly more than overlapped. The ratio of the dielectric constant of the filling dielectric to that of air in the spherical cavities was 3.5. The reported band gap only occurred in this particular structure, despite the fact that a wide variety of filling fractions and dielectric ratios were tried. It is now believed, however, that the results of that experiment were in error, and that a photonic band gap does indeed not exist in the lowest bands for dielectric spheres arranged in the fcc structure.
The present inventors have pointed out the error of that experiment and have proposed a diamond lattice crystal structure capable of achieving a true photonic band gap in a paper entitled "Existence Of A Photonic Gap In Periodic Dielectric Structures", by K. M. Ho et al., Physical Review Letters, Vol. 65, No. 25, pp. 3152-3155 (Dec. 17, 1990). The structures proposed in that paper have been further developed in a paper entitled "Photonic Band Gaps In Experimentally Realizable Periodic Dielectric Structures", by C. T. Chan et al., Europhysics Letters, 16(6), pp. 563-568 (Oct. 7, 1991).
In all cases, however, the periodic dielectric structures which have been proposed are difficult to build in the micron or submicron length scales. For example, with respect to the diamond structure discussed in these papers, the structure could be composed of dielectric spheres suspended in another material (such as air), but the suspension of the spheres in the diamond crystal structure would be difficult. As an alternative, semi-spherical holes could be drilled in dielectric slabs, and the slabs arranged to locate the holes in the required diamond structure. In that case, six holes would be required in each slab (for each crystal), and three of the holes would be relatively easy to drill, but the other three quite difficult. In addition, it is difficult when drilling holes in the micron and submicron length scales, particularly very elongated holes, to maintain the diameters exactly the same, and the crystal structure would suffer as a result.
The more recent of the two papers proposes linking of lattice sites in the crystal by means of elongated rod, and while that is a constructional improvement over the previous proposals, it is still a structure which is not readily buildable.
Thus, while theory has proposed a number of dielectric structures capable of producing photonic band gaps, the actual experiments which have resulted from the papers have utilized crystal structures which are difficult to build with precision, because of the difficulty of positioning the dielectric materials in the desired orientations with respect to each other.